Computational mechanics at the mesoscale

Abstract Conventional continuum mechanics models of inelastic deformation processes are size scale independent. In contrast, there is considerable experimental evidence that plastic flow in crystalline solids is inherently size dependent over a size scale that ranges from a fraction of a micrometer to 100 μm or so. It is over this mesoscale size range that key deformation and fracture processes in a variety of structural and electronic materials take place. Computational studies play a central role in the development of a mesoscale theoretical framework because size dependent phenomena come into play when there are gradients of deformation and stress, so that numerical methods are usually needed to obtain solutions. Three mesoscale continuum formulations are discussed, each involving a length scale and each having a different character: (i) discrete dislocation plasticity, (ii) nonlocal plasticity and (iii) the coupling of matter diffusion and deformation. The main focus is on illustrating the capability of such frameworks to elucidate aspects of material behavior that are not amenable either to a direct atomistic analysis or to a size independent continuum analysis. Numerical implementation issues are also discussed.